CECyT “Juan de Dios B´atiz” Academia de Matem´aticas
Reglas de derivaci´on.
(1) d
dx (f(x) + g(x)−h(x)) = d
dx f(x) + d
dx g(x)−d
dx h(x)
(2) d
dx (c·f(x)) = c·d
dx f(x)
(3) d
dx (c)=0
(4) d
dx un=nun−1·du
dx
(5) d
dx ln u=1
u·du
dx
(6) d
dx eu=eu·du
dx
(7) d
dx au=auln a·du
dx
(8) d
dx uv=vuv−1·du
dx +uvln u·dv
dx
(9) d
dx sen u= cos u·du
dx
(10) d
dx cos u=−sen u·du
dx
(11) d
dx tan u= sec2u·du
dx
(12) d
dx cot u=−csc2u·du
dx
(13) d
dx sec u= sec utan u·du
dx
(14) d
dx csc u=−csc ucot u·du
dx
(15) d
dx arc sen u=1
√1−u2·du
dx
(16) d
dx arc cos u=−1
√1−u2·du
dx
(17) d
dx arc tan u=1
1 + u2·du
dx
(18) d
dx arc cot u=−1
1 + u2·du
dx
(19) d
dx arc sec u=1
u√u2−1·du
dx
(20) d
dx arc csc u=−1
u√u2−1·du
dx
(21) d
dx (u·v) = u·dv
dx +v·du
dx
(22) d
dx (u·v·w) = du
dx ·v·w+u·dv
dx ·w+u·v·dw
dx
(23) d
dx u
v=
v·du
dx −u·dv
dx
v2
(24) d
dx fg(x)=df
dg ·dg
dx
(24) d
dx fgh(x)=df
dg ·dg
dh ·dh
dx
Formas elementales ordinarias de integraci´on.
(1) Z(du +dv −dw) = Zdu +Zdv −Zdw.
(2) Za du =aZdu.
(3) Zdx =x+C.
(4) Zundu =un+1
n+ 1 +C. (n6=−1)
(5) Zdu
u= ln u+C. (0 < u)
(6) Zeudu =eu+C.
(7) Zaudu =au
ln a+C.
(8) Zsen u du =−cos u+C.
(9) Zcos u du = sen u+C.
(10) Ztan u du =−ln cos u+C= ln sec u+C.
(11) Zcot u du = ln sen u+C.
(12) Zsec u du = ln(sec u+ tan u) + C.
(13) Zcsc u du = ln(csc u−cot u) + C.
(14) Zsec2u du = tan u+C.
(15) Zcsc2u du =−cot u+C.
(16) Zsec utan u du = sec u+C.
(17) Zcsc ucot u du =−csc u+C.
(18) Zdu
u2+a2=1
aarctan u
a+C.
(19) Zdu
u2−a2=1
2aln u−a
u+a+C. (u2> a2)
(20) Zdu
a2−u2=1
2aln a+u
a−u+C. (u2< a2)
(21) Zdu
√a2−u2= arc sen u
a+C.
(22) Zdu
u√u2−a2=1
aarc sec u
a+C.
(23) Zdu
√u2±a2= ln u+pu2±a2+C.
(24) Zpa2−u2du =u
2pa2−u2+a2
2arc sen u
a+C.
(25) Zpu2±a2du =u
2pu2±a2±a2
2ln u+pu2±a2+C.
C´alculo Integral Formas elementales ordinarias P´agina 1
